The Dirichlet Boundary Value Problem in Strongly Perforated Domains with Complex Boundary

Part of the Progress in Mathematical Physics book series (PMP, volume 46)


In this chapter, we study the asymptotic behavior of solutions of the Dirichlet problem in domains ω(s)=ω/F (s) , where ω is some fixed domain in ℝ n (n≥2) and F (s) (s=1, 2,…) are arbitrary closed sets. In contrast with the preceding chapter, where the sets F (s) =U i=1 s F i (s) consisting of disjoint components F i (s) , “grains,” have been considered, here the main attention is focused on connected sets F (s) . Typically, such sets consist of thin (generally, intersecting) fibers forming weblike structures.


Variational Problem Dirichlet Problem Weak Limit Orlicz Space Complex Boundary 
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© Birkhäuser Boston 2006

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